Power triangle and power factor calculator
Enter the volts, the amps and the power factor. You get apparent power (kVA), real power (kW), reactive power (kVAR) and the angle between them — and the triangle drawn to scale, so you can see what a poor power factor costs.
Three-phase: line-to-line volts and line amps, balanced load. Drawn lagging, the usual case for motors.
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How it works
- S = V × I× √3 for three-phase · VA
- P = S × PFwatts — the work
- Q = √(S² − P²)VAR — the back-and-forth
The supply has to deliver every amp the load draws — that is apparent power, S, in volt-amps. Only part of it turns into heat, light or shaft work — real power, P, in watts. The rest, reactive power Q, flows into coils’ magnetic fields and back out every cycle. P and Q are at right angles, so S is the hypotenuse, and the power factor is the cosine of the angle between S and P: PF = P ÷ S = cos θ.
Worked examples
Single-phase: 240 V, 20 A, PF 0.8
- S = 240 × 20 = 4.8 kVA.
- P = 4.8 × 0.8 = 3.84 kW.
- Q = √(4.8² − 3.84²) = √(23.04 − 14.75) = 2.88 kVAR — a 3-4-5 triangle.
- θ = cos⁻¹(0.8) = 36.9°.
Three-phase: 480 V, 50 A, PF 0.85
- S = √3 × 480 × 50 = 1.732 × 24,000 = 41.57 kVA.
- P = 41.57 × 0.85 = 35.33 kW.
- Q = 41.57 × sin(cos⁻¹ 0.85) = 41.57 × 0.527 = 21.90 kVAR.
- θ = 31.8°. The same numbers on a 600 V system scale with the voltage.
Questions people ask
What is power factor, in one line?
The share of the current that does real work: PF = kW ÷ kVA. At 1.0 every amp is doing work; at 0.8 you are carrying 1.25 amps for every amp’s worth of work (1 ÷ 0.8).
Why is three-phase multiplied by √3?
On a balanced three-phase load measured with line-to-line volts and line amps, the three phases together deliver √3 × V × I volt-amps, not 3 × V × I, because the line-to-line voltage is already √3 times each phase’s voltage in a wye (or the line current is √3 times the phase current in a delta). The three-phase lesson walks through it.
Does the calculator know if my power factor is lagging or leading?
The triangle is the same size either way; it is drawn lagging (the usual case — motors, transformers, ballasts) with the kVAR side pointing down. A leading power factor comes from capacitance and flips that side up.
Related
- Power factor and the power triangle — the lesson behind this tool.
- Intro to three-phase — the lesson behind this tool.
- Power factor — in the glossary.
- Reactance calculator — where the VARs come from.
- Reading a motor nameplate — where PF and efficiency are printed.
- Single & three phase formula sheet
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